A chemist is making a solution that is to be 55% chlorine. He has one solution that is 40% chlorine and another that is 65% chlorine. He wants 100 liters of the final solution. How much of each should he mix?
You need to mix 40 L of 40% solution and 60 L of 65% solution.
You know that the volume of the final solution is 100 L. If
Now you need to focus on the chlorine content. Since the first solution is 40% chlorine, then for
The same can be said for the 65% solution
The final solution has a percent concentration of 55% chlorine, which means that it must contain
The second equation you can write will thus relate the amount of chlorine each solution contributes to the final solution
This is your system of equations
Use the first one to write
Now use this expression in the second equation to get the value of
This means that
So, if you mix 40 L of a 40% chlorine solution with 60 L of a 65% chlorine solution you will get 100 L of a 55% chlorine solution.